Revert mount_path parameter from FastMCP

[Kludex]

Summary

This PR reverts the mount_path parameter added in #540. The parameter was redundant because the SSE transport already handles sub-path mounting via ASGI's standard root_path mechanism.

Why this revert?

When using Starlette's Mount("/path", app=mcp.sse_app()), Starlette automatically sets root_path in the ASGI scope. The SseServerTransport already uses this to construct the correct message endpoint path (see sse.py lines 148-161):

# From sse.py - this already exists and handles the issue
root_path = scope.get("root_path", "")
full_message_path_for_client = root_path.rstrip("/") + self._endpoint

Minimal Reproducible Example

The existing test test_sse_client_basic_connection_mounted_app in tests/shared/test_sse.py already demonstrates this works. Here's a simplified version:

from starlette.applications import Starlette
from starlette.routing import Mount
from mcp.server.fastmcp import FastMCP
from mcp.client.sse import sse_client
from mcp.client.session import ClientSession

# Create MCP server
mcp = FastMCP("GitHub API")

@mcp.tool()
def hello() -> str:
    return "Hello from GitHub!"

# Mount at /github sub-path - NO mount_path parameter needed!
app = Starlette(routes=[Mount("/github", app=mcp.sse_app())])

# Run with uvicorn, then connect:
async with sse_client("http://localhost:8000/github/sse") as streams:
    async with ClientSession(*streams) as session:
        result = await session.initialize()
        print(f"Connected to: {result.serverInfo.name}")
        # Works! The SSE transport automatically uses root_path
        # to return /github/messages/ as the message endpoint

The client connects to /github/sse and the server automatically returns /github/messages/ as the message endpoint - no mount_path configuration needed.

What's removed

• mount_path setting from Settings class
• mount_path parameter from FastMCP.__init__
• mount_path parameter from run() and run_sse_async()
• _normalize_path() helper method
• mount_path parameter from sse_app()
• Related tests for the removed functionality

What's updated

The README documentation now shows the correct way to mount multiple MCP servers, which works out of the box via ASGI's root_path.

[felixweinberger]

LGTM, but do we need a migration.md line about removing this?

I think it's a breaking change to remove the mount_path argument if someone was using it (even if it was redundant / did nothing).